Question

Let us assume that there are two identical conducting spheres M and N that have charges $q_m$ and $q_n$ respectively. Let a third similar neutral sphere, P , be brought in contact with M and then separated. Now sphere P is brought in contact with N and then it is made separated. Then what will be the final charge on sphere P?
$\begin{array}{rl}& A.{\displaystyle \frac{q_m+2q_n}{6}}\\ & B.{\displaystyle \frac{q_m+q_n}{4}}\\ & C.q_m+{\displaystyle \frac{q_n}{4}}\\ & D.{\displaystyle \frac{q_m+2q_n}{4}}\end{array}$

Answer 1

Hint: First of all find the charge acquired by the sphere P when kept in contact with the sphere M. initially the charge on the sphere P will be zero. Then calculate the charge acquired by the sphere P when kept in contact with the sphere N. this time the initial charge will become equal to the charge acquired by the sphere P when kept in contact with sphere M.

Complete step by step solution:
The charge on the sphere M has been given as $q_m$ and the charge on the sphere N has been given as $q_n$.
When the sphere P is brought in contact with the sphere M, then the charge on P will become,
$q_p={\displaystyle \frac{0+q_m}{2}}$
Initially the charge of the sphere P will be zero.
After making the two spheres to be in contact, the charge on the sphere P will become,
$q_p={\displaystyle \frac{q_m}{2}}$
Now the sphere P is brought in contact with N the amount charge will get varied in both the spheres. During this process initially the sphere P will be having a charge mentioned as,
$q_p={\displaystyle \frac{q_m}{2}}$
And initially the charge in the sphere N will be mentioned as $q_n$.
Therefore after making these sphere in contact, the charge on the sphere P will become,
${q^{\prime }}_p={\displaystyle \frac{{\displaystyle \frac{q_m}{2}}+q_n}{2}}$
Simplifying this will give,
${q^{\prime }}_p={\displaystyle \frac{q_m+2q_n}{4}}$
Therefore the final charge on the sphere will become,
${q^{\prime }}_p={\displaystyle \frac{q_m+2q_n}{4}}$
Hence the answer for the question has been calculated.

This answer has been given as option D.

Note:
Electric charge is defined as the basic physical characteristic of matter that will cause it to experience a force if it is placed in an electromagnetic field. There are two kinds of electric charges. One is classified as positive and the other is as negative.